The proof of Theorem REF  combines a slight adaptation of the proof for the superposition principle in \(\mathbb {R}^\mathbb {N}\)  found in [1]}, developed for use in metric measure spaces, with a finite-dimensional result for vector fields over \(\mathbb {R}^n\)  found in [2]}. Due to the strong similarities with the proof found in [1]}, we merely give a brief sketch.
